This You Tube video highlights the issues:
If anything tonight’s episode adds more to the error as during Utopia it transpires that Jack is carrying the Doctor’s hand in his bag – and yet as the camera pulls back at the end of End of Days, the Doctor’s hand is still sitting in the hub.
There has been quite a bit of speculation as to whether the TARDIS appearing at the start of Utopia and Captain Jack leaving in End of Days are the same, or different events. I was leaning towards them being the same event, but with a continuity hiccup between the two series. However with the Master taking the TARDIS at the end of Utopia, which includes the container with the Doctor’s hand – plus the knowledge that the Master is Mr Saxon and has been around for a while on Earth, maybe Gwen’s line at the end of End of Days is absolutely right – he has been taken, deceived by the the Doctor’s hand reacting to the presence of itself – and the Captain Jack who climbs aboard the TARDIS in Utopia is a future Jack…
Of course, it could just be one great big continuity mistake, but with the somewhat intricate plotting that Russell T puts in place for these story arcs – references to Mr Saxon go right back to Love and Monsters – I’d be surprised if he let such a significant continuity error through.